MPRAMunich Personal RePEc Archive

Strategic Information Transmissionthrough the Media

Hanjoon Michael Jung

Lahore University of Management Sciences

August 2007

Online at http://mpra.ub.uni-muenchen.de/5556/MPRA Paper No. 5556, posted 2. November 2007

Strategic Information Transmissionthrough the Media

Hanjoon Michael Jung�y

Department of Economics, Lahore University of Management SciencesOpposite Sector, DHA, Cantt, Lahore, Pakistan

November 2, 2007

Abstract

We model media manipulation in which a sender or senders manipulate in-formation through the media to in�uence receivers. We show that if there isonly one sender who has a conditional preference for maintaining its credibil-ity in reporting accurate information and if the receivers face a coordinationsituation without information about their opponents�types, the sender couldin�uence the receivers to make decisions according to the sender�s primarypreference by manipulating the information through the media, which makesthe report common knowledge. This is true even when the sender and thereceivers have contradictory primary preferences. This result extends to thecases in which the sender has imperfect information or in which the sender�sprimary preference is to maintain its credibility. In the case of multiple senders,however, when there is enough competition among the senders or when simul-taneous reporting takes place, the receivers could play their favored outcomeagainst senders�preferences, which sheds light on a solution to the media ma-nipulation problem.Journal of Economic Literature classi�cation numbers: C72, D82, D83.Keywords: Arms Race, Common Knowledge, Information Transmission,

Media Bias, Media Competition, Media Manipulation.

�I am very grateful to James Jordan for his guidance and encouragement. I am grateful toKyung Hwan Baik, Kalyan Chatterjee, Edward Green, Neil Wallace and anonymous referees fortheir valuable suggestions. I also wish to thank Gaurab Aryal, Sophie Bade, Frank Dardis, QiangFu, Isa Hafalir, Emin Karagozoglu, Vijay Krishna, Byung Soo Lee, Pei-yu Lo, Jawwad Noor, andEun-a Park for helpful discussions and comments.

yEmail address: hanjoon@lums.edu.pk

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1 Introduction

With rapid development of technology, the mass media have become an in�uentialforce in our daily lives as a means of information transmission. Without a systematicframework to analyze the e¤ect of the media, we are unaware of the impact of mediaand are subject to their hidden yet powerful in�uence. This paper intends to make aninitial contribution to the understanding of the systematic operation and the impactof the media. More speci�cally, this paper provides several simple models in which asender or senders manipulate information through the news media, such as newspaperor television stations, in order to in�uence the decision-making process of receivers.The setting of the models can be a general coordination game with incomplete

information. Here, an arms race game is adopted as the setting of the models notonly because it simpli�es the model while clearly showing the power of the media,but also because the results from this setting can easily be generalized into a generalcoordination game with incomplete information. In the arms race game, there aretwo players, player 1 and player 2, each simultaneously choosing to build weapons ornot to build weapons. In this game, player 2 has two possible types, either hawkishor dovish. If player 2 is hawkish, she wants to occupy a leading military positionand therefore regards building weapons as a dominant action. If player 2 is dovish,she wants to maintain a harmonious relationship with player 1. Thus, dovish player2 prefers not to build weapons as long as player 1 does not build weapons. As adovish player who also wants to defend herself, however, dovish player 2 prefers tobuild weapons if player 1 builds weapons. In other words, dovish player 2 wants tomatch the action of player 1. Player 2�s type is her own private information. On theother hand, player 1 is always dovish, so she always wants to match the action ofplayer 21. In this arms race game, there are two possible equilibrium outcomes: thebuilding-weapons outcome in which both players choose to build weapons and the not-building-weapons outcome in which both players choose not to build weapons. Here,the not-building-weapons outcome is the favorite outcome for the dovish players.In the basic model, I introduce a sender into the arms race game. The sender

has the information about player 2�s type and would report the information to play-ers 1 and 2 before they make decisions on weapon building. The following threeassumptions about the sender lead to the unique outcome of this game. First, thesender reports the information about player 2�s type through news media. By thenature of the news media, the report from the sender is commonly known to bothplayers. Second, the sender has a preference for player 1 to build weapons. Finally,the sender has a conditional preference2 for maintaining its credibility in reporting

1In the classic arms race game, both players have two possible types. By designating one player�stype as permanent, I simplify the classic arms race game while preserving the same results as theclassic models.

2This model can be considered as a simpli�ed version of the repeated game in which a senderhas two possible types: neutral or biased. A neutral sender always reports truthfully, while on theother hand, the sole concern of a biased sender is to make player 1 build weapons. In this repeated

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accurate information. Whether a sender can successfully in�uence the players or notis determined by the players�own strategies. If player 1 uses a strategy to ignorethe sender�s report and consequently the sender cannot in�uence player 1 to buildweapons, the sender would choose to preserve its credibility and thus report truthfulinformation about player 2�s type. However, if the sender can successfully a¤ect player1 to build weapons, then maintaining its credibility in reporting accurate informationis no longer a concern to the sender and it could report untruthful information. Withthis sender in the arms race game, the basic model3 shows that the only outcome inthe Perfect Bayesian equilibrium, introduced by Fudenberg and Tirole (1991), is thebuilding-weapons outcome.To see why the players cannot achieve the not-building-weapons outcome in equi-

librium, suppose that player 1 tries not to build weapons regardless of the report fromthe sender. Under this strategy of player 1, the sender cannot in�uence player 1 tobuild weapons, so the sender would report truthful information about player 2�s type.Then when the sender reports that player 2 is hawkish, player 1 is certain that player2 is hawkish and thus would build weapons. Accordingly, player 1 has an incentive tochange her action from not building weapons to building weapons in order to matchplayer 2�s action. Therefore, in equilibrium, player 1 cannot completely ignore thereport from the sender. Once player 1 responds to the sender�s report, the sender canin�uence player 1 to build weapons by manipulating the information.The result derived from the basic model shows that news media could be a pow-

erful means of information transmission. By reporting through the news media, thesender can make player 1 build weapons in accordance with the sender�s preference,and therefore players 1 and 2 lose the not-building-weapons outcome, which is a fa-vorite outcome of the dovish players. In addition, this result is strong because itis robust against two parameters. The result is robust against the probability thatplayer 2 is hawkish. It is also robust against the payo¤s to the dovish players whenthey achieve the not-building-weapons outcome. That is, no matter how small, butpositive, the probability of player 2�s being hawkish or no matter how great the pay-o¤s to the dovish players in the not-building-weapons outcome, players 1 and 2 cannotachieve the not-building-weapons outcome.Moreover, this result is stable from two aspects. First, even if we introduce a

cheap-talk between players 1 and 2 into the basic model, this result does not change.This is because if the players try to make their decisions according to their cheap-talk,then the sender cannot in�uence the players, which means that the sender�s primary

game, in response to the behavior that player 1 tries to distinguish a neutral sender from a biasedsender, a biased sender pretends to be neutral in order to preserve its in�uence on player 1. In thebasic model, to re�ect this behavior of the biased sender, the concept of credibility is adopted andadapted so that the sender considers its credibility only conditionally. For more information aboutcredibility in static games, see Kartik, Ottaviani, and Squintani (2006).

3This basic model can be exempli�ed by the Hitler�s regime in the World War II. According toShirer (1990), German citizens (player 1) openly objected to the war with the Poles (player 2). But,Hitler (the sender) successfully manipulated German citizens�opinions through the news media.

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preference cannot be satis�ed. Thus the sender would reveal the information becauseof its conditional preference. As a result, the players have an incentive to change theirstrategies, and eventually the sender can successfully in�uence the players to play thesender�s favored outcome. Second, the setting of the model, the arms race game,can be replaced with a general coordination game with incomplete information4. Inthe general coordination game with incomplete information, if the following threeconditions hold, then the result will be similar to the result in the basic model. First,in the general coordination game without a sender, the sender�s favored outcomemust be a possible equilibrium outcome when each player is a normal type, whodoes not have a dominant action; in the basic model, the sender�s primary preferenceis to make player 1 build weapons and the building-weapons outcome is a possibleequilibrium outcome when both players are dovish types, who do not have a dominantaction. Second, when each player is normal, the sender�s favored outcome consistsof each player�s strict best responses, that is, each player strictly prefers to stick toher action as long as the others do; in the basic model, each dovish player strictlyprefers to build weapons if the other does so. Third, one of the receivers�types has adominant action that is part of the sender�s favored outcome; to build weapons, in thebasic model, is a dominant action of hawkish player 2 and it is part of the sender�sfavored outcome, the building-weapons outcome. Under these three conditions, inthe general coordination game5 with a sender, the normal players and the types whohave dominant actions that are part of the sender�s favored outcome play the sender�sfavored outcome. Note that it is also possible that one of the players in the generalgame becomes a sender and sends its own information.Furthermore, this result di¤ers from the results in existing literature on informa-

tion transmission. Crawford and Sobel (1982) and Kartik, Ottaviani, and Squintani(2006) showed that if a sender and receivers have contradictory preferences, then thesender cannot in�uence the receivers to play the sender�s favored outcome (see alsoMilgrom, 1981; Sobel, 1985; and Krishna and Morgan, 2001). The basic model, on

4For simplicity, the general coordination game is assumed to satisfy the following conditions. i)Each player has one or several types including a normal type who does not have a dominant actionand the realizations of the players�types are independent. ii) When every player is normal, theysolve a coordination game, and when a player is not normal, she has a dominant action.

5For an example of the general coordination game with incomplete information, we can introducea blindly peaceful type for player 2, who will not build weapons in any case, into the arms race game.In this example, if the probability that player 2 is blindly peaceful is not so high that the building-weapons outcome is a possible equilibrium outcome, and then all types except the blindly peacefultype build weapons in an equilibrium outcome according to the primary preference of the sender.Besides, this result does not change even when we introduce a cheap-talk between players 1 and 2into this example. This is because the sender has the conditional preference for its credibility andthus the players cannot completely ignore the report from the sender in equilibrium. Therefore, inthese examples, the sender can manipulate information through the media so that the players playits favored outcome. The same is true with the opposite assumption. If the not-building-weaponsoutcome is a possible equilibrium outcome and the sender�s primary preference is to make player 1NOT build weapons, then in an equilibrium outcome, player 1 does not build weapons in any case.

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the other hand, shows that if receivers play the coordination game with incompleteinformation that satis�es the aforementioned three conditions, such as an arms racegame in the basic model, and a sender has a conditional preference on its credibil-ity and reports its information through news media, then the sender can in�uencethe receivers to play the sender�s favored outcome even when there are contradictorypreferences between the sender and the receivers.The setting of the model, the arms race game, is developed from Schelling (1960)

and Baliga and Sjöström (2004). Schelling argued that reciprocal fear from surpriseattack makes defensive action desirable and can cause a multiplier e¤ect in which bothsides generate and escalate negative expectations of their opponents. This multipliere¤ect induces arms race even when the probability of each side being hawkish is nothigh. Baliga and Sjöström formally modeled Schelling�s insight. The aforementionedarms race di¤ers from Baliga and Sjöström in that uncertainty lies only on one sideand thus there is no multiplier e¤ect. Even so, the basic model still shows that anarms race is always triggered by the sender�s will because the sender uses the mediaas a means of information transmission and it has the conditional preference.In this study, reports are relevant to payo¤s, and this property evidently dis-

tinguishes this model from the cheap-talk games developed by Farrell and Gibbons(1989a), Farrell and Rabin (1996), and Battaglini (2002). In cheap-talk games, talkis irrelevant to payo¤s. So, one player does not need to believe what other playerstalk about, and as a result only if they have a common interest in a degree, theircheap-talk can be e¤ective (see also Farrell and Gibbons, 1989b; Stein, 1989; Farrell,1993; Baliga and Morris, 2002; and Aumann and Hart, 2003; and Goltsman, Hörner,Pavlov, and Squintani, 2007). In the basic model, on the other hand, the payo¤s tothe sender depend on its report as well as on another player�s action. This is doneby assuming that the sender wants to preserve its credibility in reporting accurateinformation. This intention of the sender for its credibility makes the report from thesender e¤ective even when the sender and the players have contradictory preferences.As a result, the sender�s intention for its credibility ironically deprives the dovishplayers of their favorite outcome. Regarding main interests, the cheap-talk gamesare typically interested in how much information can be delivered in such limitedsituations. On the other hand, the basic model does not address this issue, yet itis intended to show how the sender can manipulate information through the mediainstead.The basic model can be categorized as a signaling game. Its contribution to the

literature of signaling games is to �nd su¢ cient conditions under which the sendercan successfully manipulate information through the media and, consequently, toprovide a systematic study about the e¤ect of the media as a means of informationtransmission. Nevertheless, the basic model di¤ers from the classical signaling gamesdeveloped by Spence (1973), Cho and Kreps (1987), and van Damme (1989) in thatthe sender reports player 2�s type. In these signaling games, senders only signal theirown types or their own intention about their future actions (see also Bhattacharya,

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1979; Milgrom and Roberts, 1986; Banks and Sobel, 1987; Manelli, 1997).Besley and Prat (2004) and Baron (2005) also studied media manipulation in

which the senders manipulate information through the media to in�uence receivers.Besley and Prat modeled a situation in which media outlets maintain a cozy relation-ship with the government. In exchange for compensation, such as a direct monetarypayment or bene�cial regulations, the media suppress embarrassing information aboutthe government. Also contributing to this topic, Baron employed information com-petition between two interest groups, each advocating their positions through newsmedia to in�uence public sentiment. In both papers, the extent to which the mediareports information determines the degree of in�uence that the media exert on thepublic, which actualizes media manipulation (see also Dyck and Zingales, 2003; andStrömberg, 2004). That is, more reports bring stronger in�uence on the public, andso the in�uence of the media on the decision of the public is exogenously modeled.In the present study, however, the in�uence of the media on the decision of the play-ers is endogenously created in equilibrium due to the coordination situation that thereceivers face and the sender�s conditional preference for its credibility.Section 3 extends the basic model by introducing imperfect information so that the

sender detects imperfect information about player 2�s type. Here, if the signal aboutplayer 2�s type indicates the true type of player 2 with su¢ ciently high probability,then the result in the basic model extends to the imperfect information model.Section 4 examines the opposite case of the basic model in terms of the sender�s

preferences. In this modi�ed model, the sender�s primary preference is to preserve itscredibility, and its conditional preference is to in�uence the decision-making process ofthe players. This is done by assuming that the sender is composed of a private mediaoutlet whose preferences on players�choices represent media bias. This assumptionleads to the fact that as long as its credibility remains intact, a pro�t-maximizingmedia outlet manipulates the information to increase the demand for its products.This modi�ed model concludes that the media outlet can manipulate information,in order to in�uence the players to play a speci�c outcome, without undermining itscredibility.Section 5 extends the modi�ed model to incorporate private media competition to

study the e¤ect of media competition on media bias. This media competition modelshows that if the pro�ts of private media outlets are a¤ected by media bias morethan by media competition, then the media outlets can successfully manipulate theinformation so that players choose the outcome that satis�es media outlets�concerns.However, when there are both media outlets who report truthfully and those whoreport untruthfully, if competition among media outlets is strong enough so thatcompetition brings su¢ cient rewards to the media outlets who report truthfully, theneventually all media outlets can be forced to report truthfully and receivers canachieve the not-building-weapons outcome. Therefore, enough competition among theprivate media outlets can e¤ectively curb their information manipulation through themedia and consequently reduce their in�uences on the receivers. Also, simultaneous

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reporting by at least two media outlets results in an outcome similar to the mediacompetition case.Section 6 presents summaries and conclusions.

2 Basic Model

In the basic model, a Ministry of Propaganda is the sender. There are three players;player 1, player 2, and the Ministry of Propaganda (M). Players 1 and 2 have theirown types. Player 2 can be either hawkish or dovish while player 1 is always dovish.The probability that player 2 is hawkish is h 2 (0; 1]. In this model, uncertainty liesonly in the type of player 2. M reports either that player 2 is hawkish (H) or thatplayer 2 is dovish (D). Players 1 and 2 each choose either to Build weapons (B) orNot to build weapons (N).This game proceeds as follows. At stage zero, Nature chooses player 2�s type.

Only M and player 2 detect player 2�s type. At stage one, M reports H or D. WhatM has reported becomes common knowledge. At stage two, players 1 and 2 eachsimultaneously choose B or N . After all actions are taken, payo¤s are realized.

Nature

M

1 1

M

1

2 2 2 2 2 2 22

1

Hawkish type Dovish type

H D H D

B

NB B

B

B

BB B

B

B

N

BNN N N

N N

NNN NB

Figure 1: Game Tree of the Basic Model

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The payo¤s to M depend on its own reports as well as the players�actions. Thatis, given a report r 2 fH;Dg of M and actions a1; a2 2 fB;Ng of the players, areal number ura1a2 denotes the payo¤ to M when M reports r and players 1 and 2choose a1 and a2, respectively. For example, uHBN denotes the payo¤ to M whenM reports H and players 1 and 2 choose B and N , respectively. While in thetraditional information transmission models studied by Crawford and Sobel (1982),Austen-Smith (1990), and Seidmann and Winter (1997), the payo¤s to a sender orsenders depend on receivers�actions only, in the present model, however, the payo¤sto M depend on both its own actions and the players�actions.Regarding its preferences, the primary preference6 of M is to make player 1 build

weapons; i:e: urBa2 > ur0Na02 for any r; r0 2 fH;Dg and a2; a02 2 fB;Ng in which

the left side term denotes the payo¤ to M when player 1 builds weapons and theright side term denotes the payo¤ to M when player 1 does not. M might have aparticular preference on player 2�s actions. In this model, however, such a preferencedoes not a¤ect results as long as the primary preference of M is to make player 1build weapons. So the preference of M on player 2�s action is omitted.In addition, when M is unable to in�uence player 1 to build weapons, the con-

ditional preference of M is to preserve its credibility. In this model, there are twopossible cases in which M might lose its credibility. In one case, M might lose itsCredibility related to Truthfulness (CT ). A hawkish player has a dominant action B.So ifM has reported H and player 2 plays N , then player 1 is certain thatM has lied,and thus M would lose its CT . Hence if M cannot a¤ect player 1 to build weaponsand expects player 2 to play N , then M prefers to choose D; i:e: uDNN > uHNN . Inthe other case, M might lose its Credibility related to Accurate Warning (CAW ). IfM expects player 2 to play B and reports D, then M would fail to warn player 1of the danger that player 2 would build weapons and thus lose its CAW . Hence ifM cannot a¤ect player 1 to build weapons and expects player 2 to play B, then Mprefers to report H; i:e: uHNB > uDNB.However, not every inequality stated above to summarize the preferences of M

a¤ects the outcomes in equilibrium. Of the aforementioned inequalities, only thefour listed below in�uence the outcomes. In this paper, emphasis is placed on theoutcomes in equilibrium. Therefore, for simplicity, only the following four inequalitiesare assumed to describe the preferences of the Ministry of Propaganda, M ;

i) uHBB > uDNN and uDBB > uHNN for the primary preference;

ii) uDNN > uHNN for CT ; and iii) uHNB > uDNB for CAW .

The payo¤s to players 1 and 2 are given by the following matrixes. In these ma-trixes, player 1 chooses a row and player 2 a column,

6In the general coordination games with incomplete information, the primary preference of Mcan be �exible. So if the general games satisfy the aforementioned three conditions, then no matterwhat M�s primary preference is, M can successfully in�uence normal receivers, who do not havedominant actions, to play M�s favored outcome.

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When player 2 is hawkish

N BN !; 3 0; 4B 2; 0 1; 1

When player 2 is dovish

N BN !; ! 0; 2B 2; 0 1; 1

Table 1: Payo¤Matrixes of Players 1 and 2

such that ! > 2 where the �rst entry in each cell is player 1�s payo¤ for the cor-responding actions and the second entry player 2�s. Player 1 is always dovish. Adovish player prefers to match the action of the other and prefers the NN outcometo the BB. For a hawkish player, B is a dominant action. So the BB outcome is theonly pure-strategy equilibrium in the left side matrix. Moreover, when both players1 and 2 are dovish, they want to match the action of the other. Consequently, in theright side matrix, there are two pure-strategy equilibria, the NN outcome and theBB. This two-player setting is similar to Baliga and Sjöström (2004).The arms race game without M could have two pure-strategy Perfect Bayesian

equilibrium outcomes. Players can achieve the BB outcomes regardless of player 2�stype in which players�expected payo¤s are ones. Also, if the probability h that player2 is hawkish and the payo¤ ! in the NN outcome satisfy that !�2

!�1 > h, then the NBoutcome when player 2 is hawkish and the NN when player 2 is dovish is a possibleoutcome combination in equilibrium. In this outcome, players 1 and 2 have theirexpected payo¤s (1� h)! and 4h+(1� h)!, respectively, and therefore both playersprefer the latter outcome combination to the former because of the higher expectedpayo¤s in the latter. Then, how does introducing M into the arms race game changethe results? Theorem 1 answers this question.

Theorem 1 Pure-strategy Perfect Bayesian equilibria exist, and in the equilibriumoutcomes players 1 and 2 choose Bs.

Proof. Here, every pure-strategy of player 1 is examined. First, let player 1 playB always; i:e: (B;B). Note that a dovish player prefers to match the action ofthe other player. On the other hand, a hawkish player has the dominant action B.Hence only player 2�s strategy under which she always plays B, i:e: (B;B;B;B),satis�es the best response to player 1�s strategy in each continuation game. Finally,player 1�s strategy (B;B) satis�es the best response to (B;B;B;B) in each continu-ation game. In this case, if uHBB > uDBB, then M prefers to report H always, i:e:(H;H). Accordingly, the strategy pro�le f(H;H); (B;B); (B;B;B;B)g is an equi-librium. Similarly, the following strategy pro�les are equilibria; if uHBB < uDBB,then f(D;D); (B;B); (B;B;B;B)g; and if uHBB = uDBB, then f(rH ; rD); (B;B);(B;B;B;B)g for rH ; rD 2 fH;Dg, where (rH ; rD) speci�es that M reports rH whenit detects a hawkish type and rD when it detects a dovish type. In all the cases,

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players always choose Bs in the outcomes. Therefore, there exists a pure-strategyequilibrium of which players choose Bs in the outcome.Second, let player 1 play B only when M has reported H; (B;N). Then only

player 2�s strategy under which she plays N only when player 2 is dovish and M hasreported D, i:e: (B;B;B;N), satis�es the best response in each continuation game.Next, the best response of M to these strategies is to report H when M detects adovish type because uHBB > uDNN , which denotes the primary preference of M .In this case, �rst, let M report D when it detects a hawkish type. Then M wouldreport D when it detects a hawkish type and would report H when it detects a dovishtype. So player 1 knows that player 2 is hawkish when M has reported D. Henceplayer 1 has an incentive to change her action from N to B when M has reported D.Consequently, the strategy pro�les that contain player 1�s strategy (B;N) and M�sstrategy under which M reports D only when it detects a hawkish type, i:e: (D;H),cannot be an equilibrium. Second, let M report H when it detects a hawkish type,then the player 1�s strategy (B;N) satis�es the best response in each continuationgame. Hence players choose Bs in this outcome.7 Therefore, if a strategy pro�le inwhich player 1 plays the strategy (B;N) is an equilibrium, then players choose Bs inthe outcome of this equilibrium.Third, let player 1 play N only when M has reported H; (N;B). Then only

player 2�s strategy under which she plays N only when player 2 is dovish and M hasreported H, i:e: (B;B;N;B), satis�es the best response in each continuation game.Next, the best response of M to these strategies is to report D when it detects adovish type because uDBB > uHNN , the primary preference of M . Similar to theprevious situation, if M takes the action H when it detects a hawkish type, then thestrategy pro�les in which player 1 plays (N;B) and M plays (H;D) cannot be anequilibrium. On the other hand, ifM reports D when it detects a hawkish type, thenplayers choose Bs in this outcome.8 Therefore, if a strategy pro�le in which player 1plays (N;B) is an equilibrium, then players choose Bs in this equilibrium outcome.Finally, let player 1 play N always; (N;N). Then only player 2�s strategy under

which she plays N only when she is dovish, i:e: (B;B;N;N), satis�es the best re-sponse to player 1�s strategy in each continuation game. Next, the best response ofM is to report H when it detects a hawkish type because uHNB > uDNB, the condi-tional preference for CAW , and to report D when it detects a dovish type becauseuDNN > uHNN , the conditional preference for CT . Hence when M has reported H,player 1 has an incentive to change her action from N to B because she is certainthat player 2 is hawkish and thus player 2 will choose B. Therefore, the strategypro�les in which player 1 plays the strategy (N;N) cannot be an equilibrium.Theorem 1 means that only the BB outcomes are possible in pure-strategy perfect

bayesian equilibrium and M successfully manipulates the information through thenews media. Therefore, introducing M into the arms race game lowers the players�

7If uHBB � uDNB holds, then f(H;H); (B;N); (B;B;B;N)g is a perfect bayesian equilibrium.8If uDBB � uHNB holds, then f(D;D); (N;B); (B;B;N;B)g is a perfect bayesian equilibrium.

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payo¤s. This result is strong in that it does not depend on h (> 0), the probabilitythat player 2 is hawkish, and ! (> 2), the payo¤ to the dovish players in the NNoutcome9. In addition, this result is stable in that any cheap-talk between players 1and 2 cannot change the result and in that the setting of the model could be replacedwith the general coordination game with incomplete information while preserving theresult similar to Theorem 1.In contrast to the outcomes in pure-strategy equilibrium, the outcomes in mixed-

strategy equilibrium can result in players choosing Ns with positive probabilities.However, a mixed-strategy equilibrium has negative features for the players. First,the expected payo¤s in mixed-strategy equilibrium is relatively small compared withthe expected payo¤s in the combination of the NN outcome and the NB. If player1 or player 2 is indi¤erent between playing B or N , then her expected payo¤ in thatinformation set is !

!�1 , which is less than 2, no matter which mixed strategy sheplays. If ! is large enough, then !

!�1 is pretty small compared with !. Second, theset of parameters that admit mixed-strategy equilibria has a small size under thefollowing assumptions. Suppose that uHBB > uDBB holds and the di¤erence betweenuHBN and uDBN , or between uHNN and uDNN is large enough. Then the set of theparameters that admit mixed-strategy equilibria has measure zero.

3 Imperfect Information

The basic model is extended to the case in which M observes an imperfect signalabout player 2�s type. So in this extended model, instead of directly detecting player2�s type, M detects a signal that is exogenously given and is correlated with player2�s type. However, the signal can be empty. If the signal is empty, then it doesnot reveal any information about player 2�s type. The probability that the signalindicates a hawkish type is pHH when player 2 is hawkish and is pDH when player2 is dovish. The probability that the signal indicates a dovish type is pHD whenplayer 2 is hawkish and is pDD when player 2 is dovish. Thus the probability thatM detects an empty signal is pHE = 1� pHH � pHD when player 2 is hawkish and ispDE = 1� pDH � pDD when player 2 is dovish.Here, M has three actions, H, D, and E. The action E denotes an empty report.

We can regard E as no new information reported. In this extended model,M has onemore option, E, than in the basic model. If M tries to report truthfully, it cannotreport anything when it detects an empty signal. Therefore, this setting re�ectsthe fact that M might report truthfully because of its conditional preference. Theother settings are the same as in the basic model except for the interpretation of theconditional preference of M .

9If ! is large enough, then players 1 and 2 have an incentive to pay M not to report anything.This incentive of the players can be an interesting topic to study. This model, however, does notaddress this topic in order to focus on the media as a means of information transmission.

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In this imperfect information model, M might report H by mistaking a dovishtype for a hawkish type. Hence player 1 does not know whether or not M gavea wrong report on purpose. As a result, M might not lose its credibility related totruthfulness when it has given a wrong report. Even then,M would lose its Credibilityrelated to Accurate Forecast (CAF ) if it fails to correctly forecast the action of player2. This is because a hawkish type has the dominant action B and by reporting H,M can forecast the action B. Accordingly, when M is unable to in�uence player 1 tobuild weapons, M prefers to report H only when it expects that player 2 would playB. In this model, therefore, the conditional preference of M is to preserve its CAF .The primary preference of M is still to make player 1 build weapons. Consequently,the following inequalities are assumed to describe the preferences10 of the Ministry ofPropaganda, M , with imperfect information;

i) uHBB > maxfuDNB; uDNN ; uENB; uENNg, uDBB > maxfuHNB; uHNN ; uENB; uENNg,and uEBB > maxfuHNB; uHNN ; uDNB; uDNNg for the primary preference; and

ii) uHNB > maxfuDNB; uENBg and uDNN > uHNN for CAF .

Theorem 2 shows that if the signal about player 2�s type is informative, thenTheorem 1 extends to the imperfect information model. More speci�cally, if pHH ,the probability that the signal correctly indicates a hawkish type, and pDD, theprobability that the signal correctly indicates a dovish type, are high enough, thenplayers 1 and 2 choose Bs in the equilibrium outcomes. De�nitions 1 and 2 prescribethe levels of informativeness of the signal at which the signal could in�uence thedecision-making process of M and player 1. Since player 2 knows her own type, thesignal does not directly in�uence the decision of player 2. Hence the conditions inDe�nitions 1 and 2 are su¢ cient to support a result similar to Theorem 1.De�nition 1 exhibits the levels of informativeness of the signal to M . The infor-

mativeness of the signal is evaluated based on the payo¤s to M .

De�nition 1 Suppose that uHNB > maxfuDNB; uENBg and uDNN > uHNN , CAF .Then the signal is said to be informative to M if the probabilities of the signals

10For Theorem 2, it su¢ ces to assume that uHBB > maxfhsHDuDNB+(1�h)sDDuDNN

hsHD+(1�h)sDD;

hsHDuENB+(1�h)sDDuENN

hsHD+(1�h)sDD; hsHEuDNB+(1�h)sDEuDNN

hsHE+(1�h)sDE; hsHEuENB+(1�h)sDEuENN

hsHE+(1�h)sDEg instead of uHBB >

maxfuDNB ; uDNN ; uENB ; uENNg; to assume that uDBB > maxfhsHDuHNB+(1�h)sDDuHNN

hsHD+(1�h)sDD;

hsHDuENB+(1�h)sDDuENN

hsHD+(1�h)sDD; hsHEuHNB+(1�h)sDEuHNN

hsHE+(1�h)sDE; hsHEuENB+(1�h)sDEuENN

hsHE+(1�h)sDEg instead of uDBB >

maxfuHNB ; uHNN ; uENB ; uENNg; and to assume that uEBB > maxfhsHDuHNB+(1�h)sDDuHNN

hsHD+(1�h)sDD;

hsHDuDNB+(1�h)sDDuDNN

hsHD+(1�h)sDD; hsHEuHNB+(1�h)sDEuHNN

hsHE+(1�h)sDE; hsHEuDNB+(1�h)sDEuDNN

hsHE+(1�h)sDEg instead of uEBB >

maxfuHNB ; uHNN ; uDNB ; uDNNg. These stronger assumptions are made for simplicity. However,they are innocuous in that they match the preferences of M , whose primary concern is to makeplayer 1 build weapons.

12

satisfy the following two inequalities;

hpHHuHNB + (1� h)pDHuHNNhpHH + (1� h)pDH

> (1)

maxfhpHHuDNB + (1� h)pDHuDNNhpHH + (1� h)pDH

;hpHHuENB + (1� h)pDHuENN

hpHH + (1� h)pDHg and

hpHDuHNB + (1� h)pDDuHNNhpHD + (1� h)pDD

<hpHDuDNB + (1� h)pDDuDNN

hpHD + (1� h)pDD. (2)

Suppose that player 1 plays the strategy that speci�es that she always plays N ,i.e. (N;N;N), and that player 2 plays the strategy that speci�es that she plays Bonly when she is hawkish, i:e: (B;B;B;N;N;N). In this case, M cannot in�uenceplayer 1 to build weapons. If M fails to correctly forecast the action of player 2, thenM gains nothing but loses its CAF . So if the signals indicate the true type of player 2with signi�cantly high probabilities, then M would truthfully report what it detects.Given the payo¤s to M , inequalities 1 and 2 provide precise levels of probabilitieswith which M prefers to report truthfully. More concretely, inequality 1 shows thatM prefers to report H when it detects a hawkish type and inequality 2 shows thatM prefers not to report H when it detects a dovish type.De�nition 2 formulates the levels of informativeness of the signal to player 1.

Similar to the case of M , the informativeness of the signal is evaluated based on thepayo¤s to player 1.

De�nition 2 The signal is said to be informative to player 1 if the probabilitiesof the signals satisfy the following two inequalities;

hpHH + 2(1� h)pDHhpHH + (1� h)pDH

>!(1� h)pDH

hpHH + (1� h)pDHand (3)

h(pHH + pHE) + 2(1� h)(pDH + pDE)h(pHH + pHE) + (1� h)(pDH + pDE)

>!(1� h)(pDH + pDE)

h(pHH + pHE) + (1� h)(pDH + pDE).

(4)

First, let M report H only when it detects the signal of a hawkish type. Theninequality 3 provides precise levels of probabilities with which player 1 prefers to playB when M has reported H. Second, let M report H only when it detects either thesignal of a hawkish type or an empty signal. Then inequality 4 provides precise levelsof probabilities with which player 1 prefers to play B when M has reported H.

Theorem 2 Pure-strategy Perfect Bayesian equilibria exist, and if the signal is in-formative to both M and player 1, then in the equilibrium outcomes players 1 and 2choose Bs.

13

Proof. It is easily seen that there exists an equilibrium that contains player 1�sstrategy (B;B;B) and player 2�s strategy (B;B;B;B;B;B), which specify that theyalways play Bs. In the outcomes of this equilibrium, players play Bs. Therefore, itsu¢ ces to show that if a strategy pro�le is an equilibrium, then players play Bs inthe outcomes of the strategy pro�le.Let player 1 play N only when M has reported E; i:e: (B;B;N). Then only

player 2�s strategy under which she plays N only when she is dovish and M hasreported E, i:e: (B;B;B;B;B;N), satis�es the best response in each continuationgame. Note that if M reports E, then its expected payo¤ is a weighted averagebetween uENB and uENN . Thus the best response of M to the players� strategiesis not to report E no matter what M detects because uHBB > maxfuENB; uENNg,the primary preference of M . Finally, player 1�s strategy (B;B;N) satis�es the bestresponse in each continuation game. Therefore, players choose Bs in this outcome.Similarly, players choose Bs in the equilibrium outcomes in which player 1 plays thestrategies (B;N;B), (B;N;N), (N;B;B), (N;B;N), or (N;N;B).Finally, let player 1 play (N;N;N). Then only player 2�s strategy under which she

plays N only when she is dovish, i:e: (B;B;B;N;N;N), satis�es the best responsein each continuation game. Under these strategies, M prefers to report H when itdetects a hawkish type and prefers not to report H when it detects a dovish typebecause the signal is informative to M . Then player 1 has an incentive to change heraction from N to B when M has reported H, because the signal is also informativeto player 1. Therefore, the strategy pro�les in which player 1 plays the strategy(N;N;N) cannot be an equilibrium.

Corollary 1 There exists " > 0 such that if minfpHH ; pDDg > 1 � ", then theoutcomes in pure-strategy Perfect Bayesian equilibrium are that players 1 and 2 alwayschoose Bs while M reports H, D, or E.

Proof. Since pDH � 1 � pHH and pHD � 1 � pDD, this result directly follows fromTheorem 2 and inequalities 1, 2, 3, and 4.We have examined and extended the basic model in which a sender�s primary

preference is to in�uence players�choices, such as by making player 1 build weapons,and its conditional preference is to preserve its credibility. In the next section, westudy how the changes of the sender�s value on its credibility a¤ects outcomes. For thispurpose, the opposite case of the basic model will be considered in which a sender�sprimary preference is to preserve its credibility and its conditional preference is toin�uence players� choices. This is done by assuming that a private media outletwho values its credibility most has its own preferences on players�choices and so theprivate media outlet tries to manipulate information.

14

4 Media Bias: Sender�s Value on its Credibility

In this modi�ed model, a private media outlet is the sender itself, and player 1 is themain audience to this media outlet. So, there are three players; player 1, player 2and the private media outlet (M). The other settings are the same as in the basicmodel except for the payo¤s to M .The payo¤s to M depend on its reports and the action of player 2. That is, given

a report r 2 fH;Dg of M and an action a2 2 fB;Ng of player 2, a real number ura2denotes the payo¤ to M when M reports r and player 2 chooses a2. This settingre�ects the fact that M is mainly an information provider and the information fromM would be evaluated in conjunction with the action of player 2. Thus the payo¤ toM is not a¤ected by the action of player 1. This payo¤ setting for the private mediaoutlet, M , could be considered the counterpart of the payo¤ setting for the Ministryof Propaganda in the basic model in terms of the action of player 1, since the payo¤to the Ministry of Propaganda is most a¤ected by the action of player 1.Furthermore, in contrast to the Ministry of Propaganda, the primary preference

of the private media outlet, M , is to preserve its credibility. Just like in the basicmodel, there are two possible cases in whichM might lose its credibility; it may lose itsCredibility related to Truthfulness (CT ) or its Credibility related to Accurate Warning(CAW ). Gentzkow and Shapiro (2006) studied the behavior of the media outletswho prefer to provide accurate information, and they presented empirical evidence ofsuch behavior. They also showed that the importance of credibility in media marketshas been emphasized by the management of media outlets. For example, Heyward(2004), president of CBS News, remarked, �Nothing is more important to CBS thanour credibility�(see also Kirkpatrick and Fabrikant, 2003; and Rather, 2004).When M can preserve its credibility, M is assumed to prefer the case in which it

correctly warns player 1 of the danger of player 2 than the case in which it correctlypredicts peace, i:e: uHB > uDN

11. This preference represents media bias. This as-sumption about the media bias re�ects the following intuition: player 2�s developingnew weapons i) makes player 1 feel more insecure; so ii) induces player 1, who is themain audience to M , to pay more attention to M ; and thus iii) eventually increasesthe pro�t ofM by expanding the demand for the products ofM . This kind of assump-tion about media bias is not new in economic literature. Mullainathan and Shleifer(2005) modeled media bias based on a similar assumption in which pro�t-maximizingmedia outlets slant news stories to increase the demand for their products.Formally, the following inequalities are assumed to describe the preferences of the

private media outlet, M ;

i) minfuDB; uDNg > uHN for CT ; ii) uHB > uDB for CAW ; andiii) uHB > uDN for the media bias.

11In the general coordination games with incomplete information, similar to the case of the basicmodel, the conditional preference of M can be �exible.

15

with these preferences of M , we can derive a result similar to Theorem 1.

Theorem 3 The unique outcome in pure-strategy Perfect Bayesian equilibrium isthat M reports H and players 1 and 2 choose Bs. If uHN is small enough, there isno mixed strategy equilibrium except pure-strategy equilibrium.

Proof. The proof of the �rst assertion is omitted because it is similar to the proofof Theorem 1.To prove the second assertion, let � be the probability with which M reports H

when it detects a dovish type. Also, let a2 and b2 be the probabilities with whichdovish player 2 chooses B when M has reported H and chooses B when M hasreported D, respectively. Finally, Let

a02 � b2uDB + (1� b2)uDN � uHNuHB � uHN

and

a002 � �(1� h)(! � 2)� h�(1� h)(! � 1) .

If a2 is equal to a02, M is indi¤erent between playing H or D when it detects a dovishtype. Also, if a2 is equal to a002, player 1 is indi¤erent between playing B or N whenM has reported H. However, given payo¤ parameters and h, if uHN is small enough,then a02 is greater than a

002 for any b2; � 2 [0; 1].

Let a1 be the probability with which player 1 chooses B when M has reportedH. First, if a2 < a02, then M prefers to play D when it detects a dovish type. Notethat M prefers to play H when it detects a hawkish type because uHB > uDB, theprimary preference for CAW . Then player 1 knows that player 2 is hawkish whenM has reported H. Hence, player 1 prefers to play a1 = 1. Second, if a002 < a2, thenplayer 1 prefers to play a1 = 1. If uHN is small enough, then a2 < a02 or a

002 < a2

because a002 < a02. Hence player 1 would play only a1 = 1, and thus player 2 of a dovish

type would also play only a2 = 1. ThenM would report only H because uHB > uDB,the primary preference for CAW , and uHB > uDN , the media bias. Therefore, thereexists only a pure-strategy equilibrium.Theorem 3 shows that even when the primary preference of the sender is its

credibility, the receivers do not bene�t more than they do in the basic model. This isbecause the availability of the information fromM removes the possibility for playersto choose Ns. Consequently, M�s warning to player 1 induces both players to chooseBs.From M�s point of view, the worst payo¤ is when it is proved to have lied. Only

the payo¤ parameter uHN denotes this worst payo¤. So, lower uHN means that Mvalues its credibility related to truthfulness, CT , more. Theorem 3 implies that morevalue placed on the sender�s CT could result in worse outcomes for the receivers byremoving a mixed-strategy equilibrium. Also, the payo¤ uHN could be consideredto be the punishment that player 1 in�icts on M when M has veri�ably lied. This

16

is because player 1 is M�s main audience and so the payo¤s to M depend largelyon player 1�s interest in M�s information. Then Theorem 3 implies that player 1cannot improve her expected payo¤ by punishing M when M has veri�ably lied andsometimes player 1 could even lower her expected payo¤ by punishing M .DeFleur and Ball-Rokeach (1989) and Morris and Shin (2002) also analyzed the

e¤ects of information from the media (see also Gamson, Croteau, Hoynes, and Sasson,1992; and Bernhardt, Krasa, and Polborn, 2006). They assumed that the degree ofin�uence that the media exert on the public is determined by the extent to which themedia reports its information, and thus the in�uence of the media on the public wasexogenously modeled. In the present model, in contrast to their works, the structureof the model endogenously creates the in�uence of the media on the players�decision-making process.We have seen two kinds of information transmission models: the basic model and

the media bias model. In both models, there is only one sender, and the senderachieves its favored outcome by manipulating information through the news media.Then, what would occur if there are more than one sender? If there are more than onesender, the senders could compete with one another. Does the competition matter inthese information transmission models? Does reporting simultaneously or reportingsequentially make a di¤erence? The next section answers these questions.

5 Media Competition: Multiple Senders

In this model, I extend the previous model by introducing another private mediaoutlet. Therefore, there are four players; player 1, player 2, media outlet 1 (M1), andmedia outlet 2 (M2). Player 1 is still the main audience to both M1 and M2. Themedia outlets report sequentially or simultaneously. When they report sequentially,M1 reports �rst. The other settings are the same as in the media bias model exceptthe payo¤s to the media outlets.The payo¤s to each outlet depend on the reports from the other outlet as well as

its own reports and the action of player 2. That is, given reports r1; r2 2 fH;Dgof the media outlets and an action a2 2 fB;Ng of player 2, a real number uir1r2a2denotes the payo¤ toMi for i 2 f1; 2g whenM1 reports r1, M2 reports r2, and player2 chooses a2. This setting allows us to examine the e¤ect of media competition.Regarding their preferences, just like in the media bias model, the primary pref-

erence of the media outlets is to preserve their credibility: CT and CAW . In thismodel, the conditional preference of the media outlets depends on both media biasand media competition. The media outlets have the same bias as in the media biasmodel. So the media outlets prefer the case in which they correctly warn player 1of the danger of player 2 than the case in which they correctly predict peace. Thefollowing inequalities represent all possible cases of media bias; minfu1HHB; u1HDBg >maxfu1DHN ; u1DDNg and minfu2HHB; u2DHBg > maxfu2HDN ; u2DDNg. Media compe-tition imposes another condition for the payo¤s to the media outlets by tempt-

17

ing them to occupy a leading position in competition. That is, in competition,media outlets have more incentive to predict correctly while others predict incor-rectly than while others also predict correctly. The following inequalities describe allpossible cases of media competition; minfu1DHN ; u1HDBg > maxfu1HHB; u1DDNg andminfu2HDN ; u2DHBg > maxfu2HHB; u2DDNg.However, the following two inequalities for media competition u1DHN > u

1HHB and

u2HDN > u2HHB directly contradict the inequalities for media bias u1DHN < u1HHBand u2HDN < u2HHB. Therefore, there are two possible cases: one case in whichbias dominates competition and the remaining case in which bias does not dominatecompetition. When bias dominates competition and the private media outlets reportsequentially, the following inequalities are assumed to describe the preferences of themedia outlets;

i) minfu2HDB; u2HDNg > u2HHN for CT ;ii) u1HHB > maxfu1DHB; u1DDBg and u2HHB > u2HDB for CAW ; andiii) u1HHB > maxfu1DDN ; u1DHNg and u2HHB > u2HDN for the media bias.

When bias does not dominate competition and the private media outlets report se-quentially, the following inequalities are assumed to describe the preferences12 of themedia outlets;

i) u1DDN > u1HDN and u

2DDN > u

2DHN for CT ;

ii) u1HHB > maxfu1DHB; u1DDBg and u2HHB > u2HDB for CAW ; andiii) u2HDN � u2HHB for the weakly dominant media competition.

Note that when bias dominates competition, u2HHB > u2HDN is assumed. On the other

hand, when bias does not dominate competition, u2HHB � u2HDN is assumed. Finally,when the private media outlets report simultaneously, the following inequalities areassumed to describe the preferences13 of the media outlets;

i) u1DDN > u1HDN and u

2DDN > u

2DHN for CT ; and

ii) u1HHB > u1DHB and u

2HHB > u

2HDB for CAW .

Theorem 4 Suppose that the media outlets report sequentially. If bias dominatescompetition, then the unique outcome in pure-strategy Perfect Bayesian equilibrium

12For Theorem 4, it su¢ ces to assume that u1DDN � u1HDN and u2DDN � u2DHN instead of u1DDN >u1HDN and u2DDN > u2DHN ; and to assume that u

1HHB � maxfu1DHB ; u1DDBg and u2HHB � u2HDB

instead of u1HHB > maxfu1DHB ; u1DDBg and u2HHB > u2HDB . These stronger assumptions are madein accordance with the preferences about credibility.13For Theorem 4, it su¢ ces to assume that u1DDN � u1HDN and u2DDN � u2DHN instead of

u1DDN > u1HDN and u2DDN > u2DHN ; and to assume that u1HHB � u1DHB and u2HHB � u2HDB

instead of u1HHB > u1DHB and u

2HHB > u

2HDB . These stronger assumptions are made in accordance

with the preferences about credibility.

18

is that both outlets report Hs and players choose Bs. In addition, if u2HHN is smallenough, there is no mixed-strategy equilibrium except pure-strategy equilibrium. How-ever, if bias does not dominate competition, then there exists a pure-strategy PerfectBayesian equilibrium in which the media outlets report Hs and players choose Bswhen player 2 is hawkish and the media outlets report Ds and players choose Nswhen player 2 is dovish. Suppose that the media outlets report simultaneously. Thenthere also exists the pure-strategy Perfect Bayesian equilibrium in which the mediaoutlets report Hs and players choose Bs when player 2 is hawkish and the mediaoutlets report Ds and players choose Ns when player 2 is dovish.

Proof. First, suppose that the media outlets report sequentially. It is easily seenthat there exists an equilibrium outcome in which players 1 and 2 play Bs. Therefore,it su¢ ces to show that if a strategy pro�le is an equilibrium, then players play Bs inthe outcomes of the strategy pro�le.Let player 1 play B when both outlets have reported Hs. Then the best response

of player 2 to this action is to play B when both outlets have reported Hs. Next, thebest response of M2 to these actions is to play H when M1 has reported H becauseu2HHB > u

2HDB, CAW , and u

2HHB > u

2HDN , the media bias. Also, the best response

of M1 to these actions is to play H because u1HHB > maxfu1DHB; u1DDBg, CAW , andu1HHB > maxfu1DDN ; u1DHNg, the media bias. Finally, the best response of player 1is to play B when both outlets have reported Hs. Therefore, in this outcome, bothoutlets report Hs and players choose Bs.Let player 1 play N when both outlets have reported Hs. Then the best response

of dovish player 2 is to play N when both outlets have reported Hs. Next, the bestresponse of M2 is to play D when it detects a dovish type and M1 has reported Hbecause minfu2HDB; u2HDNg > u2HHN , CT . Note that if the media outlets detect ahawkish type, then they know that player 2 would play B, and thus they prefer toreport Hs because u2HHB > u2HDB and u

1HHB > maxfu1DHB; u1DDBg, CAW . Hence,

player 1 can be certain that player 2 is hawkish when both outlets have reported Hs.Consequently, player 1 has an incentive to change her action from N to B when bothoutlets have reported Hs. Therefore, a strategy pro�le in which player 1 plays Nwhen both outlets have reported Hs cannot be an equilibrium. This completes theproof of the �rst assertion.The proof of the second assertion is omitted because it is similar to the proof in

Theorem 3.To prove the third and the fourth assertions, let player 1 play B only when both

outlets have reportedHs; i:e: (B;N;N;N). Then only player 2�s strategy under whichshe plays B either when she is hawkish or when both outlets have reported Hs, i:e:(B;B;B;B;B;N;N;N), satis�es the best response in each continuation game.Suppose that bias does not dominate competition. Then when M2 detects a

dovish type, one of the best responses of M2 is to report D no matter what M1 hasreported because u2DDN > u2DHN , CT , and u

2HDN � u2HHB, the weakly dominant

media competition. Next, when M1 detects a dovish type, the best response of M1

19

is to report D because u1DDN > u1HDN , CT . Note that if M1 detects a hawkishtype, then it would report H because u1HHB > maxfu1DHB; u1DDBg, CAW . Also,if M1 has reported H and M2 detects a hawkish type, then M2 would report Hbecause u2HHB > u2HDB, CAW . Under these strategies of player 2, M1, and M2,player 1�s strategy (B;N;N;N) satis�es the best response in each continuation game.Therefore, there exists an action r2HD 2 fH;Dg of M2 such that the strategy pro�lef(H;D); (H; r2HD; D;D); (B;N;N;N); (B;B;B;B;B;N;N;N)g is an equilibrium,where r2D speci�es the action of M2 when it detects a hawkish type and M1 hasreported D. In this strategy pro�le, the media outlets report Hs and players chooseBs when player 2 is hawkish and the media outlets report Ds and players choose Nswhen player 2 is dovish.Finally, suppose that the media outlets report simultaneously. Then when the

outlets detect a hawkish type, each outlet prefers to report H if the other outletwould report H because u1HHB > u1DHB and u2HHB > u2HDB, CAW . Also, whenthe outlets detect a dovish type, each prefers to report D if the other would reportD because u1DDN > u1HDN and u2DDN > u2DHN , CT . Finally, player 1�s strategy(B;N;N;N) satis�es the best response in each continuation game. Therefore, thestrategy pro�le f(H;D); (H;D); (B;N;N;N); (B;B;B;B;B;N;N;N)g is a pure-strategy equilibrium and in this equilibrium the media outlets report Hs and playerschoose Bs when player 2 is hawkish and the media outlets report Ds and playerschoose Ns when player 2 is dovish.Therefore, as long as bias dominates competition and the media outlets report

sequentially, players 1 and 2 cannot improve their expected payo¤s. Just like in themedia bias model, the punishment for an untruthful report does not improve players�expected payo¤s, and sometimes even lowers their payo¤s. However, media competi-tion and simultaneous reporting each can make the media outlets report truthfully,and consequently players can improve their expected payo¤s. In fact, the outcomecombination in which players 1 and 2 play Bs when player 2 is hawkish and theyplay Ns when player 2 is dovish gives player 1 the best payo¤ out of all outcomecombinations such that hawkish player 2 plays B, and player 1 can achieve this com-bination only when the media outlets reveal the information about player 2�s type.Also, when there are more than one sender in the basic model, if the senders reportsimultaneously or if competition among the senders is strong enough, then playerscan achieve this outcome combination. Therefore, enough competition and si-multaneous reporting can each solve media manipulation problems in thisstudy.The media competition model can be extended by introducing more media outlets

and imperfect signals about player 2�s type. In this case, if bias dominates competi-tion, then we can derive a result similar to Theorems 2 and 4. That is, if the signalis informative to player 1 and to the media outlets, then the unique outcome in pure-strategy equilibrium is that all outlets report Hs and players choose Bs. However, ifcompetition dominates bias, then the result depends on media outlets�herd behavior

20

in reporting, which was studied by Scharfstein and Stein (1990) and Banerjee (1992),and the result might di¤er from Theorems 2 and 4. Here, herd behavior in reportingmeans that media outlets just follow other outlets�actions regardless of their owninformation about player 2�s type.To see how the result can be a¤ected by the herd behavior, suppose that player

1 plays N if at least one media outlet reports D. If competition dominates biasand there is no herd behavior, then this strategy of player 1 in�uences the mediaoutlets to report truthfully. However, in the imperfect information case, when mediaoutlets truthfully report and it turns out that only one outlet has reported D andthe other all outlets have reported Hs, player 1 has an incentive to change her actionfrom N to B. This is because the probability that player 2 is hawkish is muchhigher than the probability that player 2 is dovish. Since player 1 would not playher strategy suggested above, the media outlets lose an incentive to report truthfully.In this case, if there is herd behavior in reporting, then even when all media outletsexcept one outlet have reported Hs, the probability that player 2 is hawkish mightnot be high. This is because most of the outlets just followed previous reports andaccordingly just a few media outlets reveal their information about player 2�s type.Consequently, if the payo¤ ! of player 1 in the NN outcome is large enough, thenplayer 1 can rationally play N even when all media outlets except one outlet havereported Hs. Therefore, player 1 can achieve her favored outcome, NN . In this sense,media outlets�herd behavior in reporting is considered to improve player 1�s expectedpayo¤.This model focuses on the e¤ect of media bias as a part of general endeavor to

understand the media as a means of information transmission. A large literatureabout the media, on the other hand, focuses on the occurrence and persistence ofmedia bias. Most of them assume irrational players to a certain extent and explainwhy media bias happens and continues based on the irrational player assumption.Mullainathan and Shleifer (2005), Baron (2006), and Gentzkow and Shapiro (2006)studied media bias and examined whether media competition can reduce media bias.Baron explained that the occurrence and persistence of media bias can arise fromthe supply side by journalists who are willing to accept lower wages for the sake oftheir discretion. Mullainathan, Shleifer, Gentzkow, and Shapiro showed that mediabias can, however, come from the demand side. They argued that pro�t-maximizingmedia outlets could cater to the preferences or prior beliefs of their audience, whocan be considered as irrational players, to increase the demand for their products;this behavior represents media bias. Regarding media competition, Mullainathan,Shleifer, and Baron concluded that competition by itself may not be powerful enoughto reduce media bias. On the other hand, Gentzkow and Shapiro found that competi-tion among independently owned media outlets can lead to lower bias. In the presentmodel, similar to Gentzkow and Shapiro, su¢ ciently strong competition can lead themedia outlets to report truthfully.

21

6 Conclusions

Suppose that receivers are in a situation of potential con�ict and a sender reportsits information through the news media. In addition, suppose that the sender has aconditional preference for maintaining its credibility in reporting accurate informa-tion. Then even when the sender and the receivers have contradictory preferences,the sender can make the receivers play the sender�s favored outcome. This resultextends to the imperfect information case. That is, when the information includesnoise, if the information is informative enough, then the sender can achieve its favoredoutcome.This result does not change even when the sender values more its credibility in

reporting accurate information. This is because the availability of the informationfrom the sender removes the possibility for the players to play Ns. However, if thereare more than one sender, then the result could change. If competition among thesenders is strong enough or if at least two senders report simultaneously, then thesenders can be forced to report truthfully, and as a result, the receivers�expectedpayo¤s can improve. Therefore, enough competition and simultaneous reporting canbe a solution to the media manipulation problem in this study.The �ndings derived from the arms race game could be extended to the general

coordination game with incomplete information where there can be more than tworeceivers and also more than two actions for each receiver. This is because, just likethe receivers in the arms race game, receivers in the general coordination games cannotcompletely ignore the report from senders. As a result, the senders can successfullyin�uence the receivers to play their favored outcome by manipulating informationthrough the media.

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